Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int a[200010];
int q[200010];
int T[200010];
int f[200010];
int n;
int cnt;

int main()
{
	cin>>n;
	for (int i=1;i<=n;i++) cin>>a[i];
	for (int i=1;i<=n;i++) q[a[i]]=i;
	
	for (int i=n-1;i;i--)  
    {  
        if( !T[ i + 1 ] )  
        {  
            if( q[i] > q[i+1] ) T[i]=1, f[i]=i+1;  
            else T[i] = 0;  
        }  
        else  
        {  
            int cnt = 0;  
            cnt += q[f[i+1]] < q[i];  
            cnt += q[i] < q[i+1];  
            cnt += q[i+1] < q[f[i+1]];  
            if (cnt==2) T[i]=T[i+1],f[i]=f[i+1];  
            else T[i]=T[i+1]+1,f[i]=i+1;  
        }  
    }  
    cout<<T[1];
}